A navigational risk evaluation of ferry transport: Continuous risk management matrix based on fuzzy Best-Worst Method

Ferry transport has witnessed numerous fatal accidents due to unsafe navigation; thus, it is of paramount importance to mitigate risks and enhance safety measures in ferry navigation. This paper aims to evaluate the navigational risk of ferry transport by a continuous risk management matrix (CRMM) based on the fuzzy Best-Worst Method (BMW). Its originalities include developing CRMM to figure out the risk level of risk factors (RFs) for ferry transport and adopting fuzzy BWM to estimate the probability and severity weights vector of RFs. Empirical results show that twenty RFs for ferry navigation are divided into four zones corresponding to their risk values, including extreme-risk, high-risk, medium-risk, and low-risk areas. Particularly, results identify three extreme-risk RFs: inadequate evacuation and emergency response features, marine traffic congestion, and insufficient training on navigational regulations. The proposed research model can provide a methodological reference to the pertinent studies regarding risk management and multiple-criteria decision analysis (MCDA).


Reviewer #2:
Comment # 1.The paper is of importance in terms of merging continuous risk matrix and Fuzzy BWM.But I wonder how the authors generate the Figure 2. I think more details needed to explain how they structured the x-and y-axis values.What is the continuous function here?Answer: Thanks so much for your comment.We would like to explain as follows: a) How the authors generate the Figure 2: From Table 5 of our manuscript, we calculated risk value (RVs) of risk factors (RFs) using Equation ( 9).As a result, the risk value of RFs is found and exhibited in the second-to-last column of Table 6.Then, this study utilized the "ggRepel" package in Rstudio to visually represent the continuous risk management matrix (CRMM), which is precisely Figure 2. b) More details needed to explain how they structured the x-and y-axis values: In Figure 2, the xaxis present probability (%) and the y-axis stand for severity (%) of risk factors.The more probability and severity, the more risk the risk factors are facing to.More specifically, 20 risk factors are divided into 4 groups: L (low), M (medium), H (high), and E (extreme) risk zones.Also, three risk factors located in the E zone include VD4, EE4, and PR3.In other words, ferry operators should pay more attention to such risk factors than others in the context of limited resources.We revised our manuscript by referring some of your suggestions (Seeing Rows 323-326).
Comment # 2. Going on from the end of comment 1, how they determine the four categories?Why four?
Answer: Thanks so much for your comment.We would like to explain as follows: a) How authors determined the four categories: From Table 5 of our manuscript, we calculated risk value (RVs) of risk factors (RFs) using Equation ( 9).As a result, the risk value of RFs was found and exhibited in the second-to-last column of Table 6.Now, we had 20 risk factors with their risk values of 5%.
Then, risk factors with were averaged to ascertain extreme-and high-risk factors.Next, Please explain in detail.
Answer: Thanks so much for your comment.We would like to explain as follows: It has been argued that risk evaluation in ferry transport is characterized as a multi-criteria decision analysis (MCDA) problem.In the case of ferry transport, where various factors contribute to the complexity of risk, MCDA allows decision-makers (DMs) to consider multiple criteria simultaneously when assessing risks.Nevertheless, some of the most common tools of MCDA, such as AHP, ANP, and SAW, require numerous pairwise comparisons (PCs) of risks, thereby not only weakening their practical application, but also increasing the inconsistency of PCs.To cope with this challenge, the Best-Worst Method (BWM) developed by Rezaei (2015) has been adopted extensively to solve MCDA.Compared with the classic tools of MCDA, the primary strength of BWM is fewer PCs, thus prone to obtaining DMs' judgment and boosting the consistency of subjective evaluation.Additionally, it is illustrated that DMs' subjective assessment is often uncertain and imprecise.Accordingly, the theory of the fuzzy set is incorporated into BWM to allow for the representation of degrees of such uncertainty and vagueness.
By the way, please seeing Rows 69-81 for more information.
Comment # 4. I think a flow chart is required to easily understand the integration between CRMM and fuzzy BWM.More theoretical information is needed for CRMM.
Answer: Thanks so much for your suggestion.We already inserted one flowchart to explain the integration between CRMM and fuzzy BWM (Seeing Rows 209-216).Besides, more theoretical information for CRMM was added (Seeing Rows 275-279).
Comment # 5. Authors provided a consistency computation in their method part but there is no output for this in the application.Please provide your results regarding consistency.
Answer: Thanks so much for your suggestion.We would like to explain that: For the application of fuzzy BWM, we assessed consistency of every judgment for every respondent.
It is worth noting to emphasise that the nature of BWM is that we cannot average expert's rating.Please seeing Rezaei (2015)1 and Mi et al. ( 2019)2 for more information.As a result, we were only able to calculate the consistency ratio (CR) for each expert in terms of each dimension (criterion).
With reference to your request, the table below shows the consistency ratio of ratings in the FO-VN case.Note that all illustrate the consistency of judgments.

Respondent
Figure a. Figure b.Empirical case: Figure c. Figure d.
risk factors with were averaged to find medium-and low-risk factors.b) Why we just categorized four: In the traditional risk matrix (i.e, DRMM), the relevant research prefers to classify risk factors into three categories, as seen Figure a, as mentioned earlier.Yet, DRMM might fail to identify true risk factors.Accordingly, our study divided risk factors into four groups to deeply understand risk factors.As a result, the proposed method (i.e., CRMR) determined three extreme risk factors for prioritizing the allocation of scarce resources while DRMM only figured out one.Comment # 3. Why the authors prefer fuzzy version of BWM?Is there a special reason or not?